Stress intensity factors and T-stresses by boundary integral equations: 3D statics

Abstract This paper presents the boundary integral equation method (BIEM) for the stress intensity factors and elasticity T-stresses evaluation in 3D problems. Flat rectangular, elliptic, penny-shaped cracks and rectangular crack on a cylindrical surface have been investigated. The hyper-singular integrals are treated with the Taylor’s series expansion of the kernel, and the Chebyshev polynomials of the second kind are used to solve the integral equations numerically. The stress intensity factors (SIFs) on the crack front are obtained by the coefficients of the Chebyshev polynomials. In order to verify the solutions by BIEM, the finite element method (FEM) with ABAQUS is conducted. The efficiency and convergence of the BIEM are observed in three examples. Comparisons are made with the analytical solutions in the stress intensity factor handbook and numerical solutions using the displacement discontinuity method (DDM).